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Volodymyr Mazorchuk (Uppsala University, Sweden)
Lectures on Algebraic Categorification
ISBN print 978-3-03719-108-8, ISBN online 978-3-03719-608-3DOI 10.4171/108
March 2012, 128 pages, softcover, 17 x 24 cm.
28.00 Euro
The term “categorification” was introduced by Louis Crane in 1995 and refers to
the process of replacing set-theoretic notions by the corresponding category-theoretic
analogues. This text mostly concentrates on algebraical aspects of the theory, presented
in the historical perspective, but also contains several topological applications,
in particular, an algebraic (or, more precisely, representation-theoretical) approach
to categorification. It consists of fifteen sections corresponding to fifteen
one-hour lectures given during a Master Class at Aarhus University, Denmark in
October 2010. There are some exercises collected at the end of the text and a
rather extensive list of references. Video recordings of all (but one) lectures are
available from the Master Class website. The book provides an introductory overview of the subject rather than a fully
detailed monograph. Emphasis is on definitions, examples and formulations of
the results. Most proofs are either briefly outlined or omitted. However, complete
proofs can be found by tracking references. It is assumed that the reader is
familiar with the basics of category theory, representation theory, topology and
Lie algebra.
Keywords: Categorification, 2-category, Lie algebra, module, category O, functor, knot, Jones polynomial, Verma module, translation functor
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